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The cavitation problem of a preexisting microvoid in the incompressible viscoelastic sphere subjected to the uniform temperature field was studied in this paper. Based on the finite logarithmic strain measure for geometrically large deformation, the nonlinear mathematical model of this problem was established by employing the Kelvin-Voigt differential type constitutive equation of thermoviscoelasticity. Adopting the dimensionless transformation of each parameter, growth curves of the microvoid radius increasing with the temperature were given. And the results indicated that the generation of cavity could be regarded as the idealized model of microvoid growth. A parametric study, including the influences of the external temperature, the initial microvoid radius, and the material parameter on the microvoid radius, was also conducted. The sudden growth of infinitely large sphere with a preexisting microvoid could also achieved by the finitely large sphere.

The cavitation problem caused by the material instability has been attracting attention of many researchers for decades. The cavitation problems of solid materials are divided into two parts, one is the sudden growth of a pre-existing microvoid in the infinitely large solid material, and the other is the sudden generation and growth of a cavity in the finitely large solid material [

Metal materials have been the main structure members of the airframe and the aircraft engine, due to the high speed flight. The fatigue life of the aviation material is seriously affected by the transient thermal stress caused by aerodynamic heating. As for the metal materials, their viscoelastic behaviors are close related to vibration or high temperature, and thus, the temperature is a key factor for the cavitation problem in the viscoelastic material. Zhang [

The mechanical characteristics are related to time in the viscoelastic material and sensitive to strain rate. Furthermore, the cavitation and bifurcation problems in the viscoelastic material are considered as the instability for nonlinear materials and also the exact solution for such a large deformation problem are very difficult. So, the purpose of this paper is to establish the nonlinear dynamical mathematical mode of the microvoid motion in an incompressible thermoviscoelastic sphere subjected to the uniform temperature field. And by the semianalytical and seminumerical method, variation curves of the microvoid radius with temperature were given. Dynamical variation curves were also obtained to describe the microvoid radius increasing with time. The influences of these parameters on the variation rules of microvoid radius were analyzed.

Consider a sphere with the pre-existing microvoid composed of incompressible viscoelastic material subjected to a uniform temperature field. Assume that the initial and current radii of the sphere are

Profile of the sphere.

The spherically symmetric motion can be expressed as

The Kelvin-Voigt differential type constitutive equations for thermo-visco-elasticity [

The differential equation of motion with the absence of body force is

The logarithmic strains are used to describe the finite deformation:

In view of the incompressibility condition of the material

The outer surface of the microvoid is traction free for the radial stress:

The free boundary condition of the outermost layer in the sphere is

Supposing the sphere is in the undeformed state at

Differentiating twice the incompressible condition (

Integrating (

Combining the boundary condition (

Then, the expressions for the radial and hoop Euler stresses are obtained:

Combining the boundary condition (

Equation (

Using the dimensionless transformation

Letting

The quasistatic solution of the thermo-viscoelastic sphere can be obtained from (

Curves of microvoid radius

Letting

Let

Letting

Combining the initial condition (

Observing (

Variation curves of microvoid radius

Variation curves of

Variation curves of microvoid radius

Variation curves of microvoid radius

Figure

Figure

Figure

In this paper, the microvoid dynamical growth problem in an incompressible thermo-viscoelastic sphere subjected to a uniform temperature field is researched. An exactly differential relation between the microvoid radius and the outside temperature field is obtained. It is concluded that it will spend shorter time for the larger initial microvoid radius with the higher temperature and the smaller parameter

The authors sincerely thank the anonymous referees for their valuable suggestions and comments; this work was supported by the National Natural Science Foundation of China (no. 10772024).